Subgroups — C₂₃×#61731 #19209357

Order 5888.

1816 conjugacy classes of subgroups.

The subgroup lattice has 880 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₃×#3520	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₂₃×#555	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂₃×#3354	C₂	1	2	yes	maximal, complemented
4	C₂₃×#3348	C₂	1	4	yes	maximal, complemented
5	C₂₃×#3340	C₂	1	2	yes	maximal, complemented
6	C₂₃×#3329	C₂	1	2	yes	maximal, complemented
7	C₂₃×#3321	C₂	1	4	yes	maximal, complemented
8	C₂₃×#3303	C₂	1	2	yes	maximal, complemented
9	C₂₃×#3238	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂₃×#3229	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂₃×#3194	C₂	1	2	yes	maximal, complemented
12	C₂₃×#3187	C₂	1	2	yes	maximal, complemented
13	C₂₃×#3110	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂₃×#3105	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂₃×#3095	C₂	1	2	yes	maximal, complemented
16	C₂₃×#3091	C₂	1	2	yes	maximal, complemented
17	C₂₃×#2974	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂₃×#556	C₂²	1	1	yes	characteristic, complemented
19	C₂₃×#555	—	2	1	no	—
20	C₂₃×#555	—	2	2	no	—
21	C₂₃×#555	—	2	1	no	—
22	C₂₃×#555	C₂²	1	2	yes	—
23	C₂₃×#555	C₂²	1	4	yes	—
24	C₂₃×#555	C₂²	1	2	yes	—
25	C₂₃×#554	—	2	1	no	—
26	C₂₃×#552	C₂²	1	2	yes	complemented
27	C₂₃×#551	—	2	2	no	—
28	D₄×Q₈×C₂₃	C₂²	1	1	yes	characteristic, complemented
29	C₂₃×#548	C₂²	1	2	yes	complemented
30	C₂₃×#547	C₂²	1	1	yes	characteristic, complemented
31	C₂₃×#547	C₂²	1	1	yes	characteristic, complemented
32	C₂₃×#546	—	2	1	no	—
33	C₂₃×#542	—	2	1	no	—
34	C₂₃×#539	—	2	2	no	—
35	C₂₃×#533	C₂²	1	1	yes	characteristic
36	C₂×C₂₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
37	C₂₃×#529	C₂²	1	1	yes	characteristic
38	C₂×C₂₃×#124	—	2	2	no	—
39	C₂₃×#525	C₂²	1	2	yes	—
40	C₂×C₂₃×C₂²⋊Q₈	C₂²	1	2	yes	—
41	C₂×C₂₃×#121	—	2	1	no	—
42	C₂×C₂₃×#121	C₂²	1	2	yes	—
43	C₂₃×#520	—	2	1	no	—
44	C₂×C₄×D₄×C₂₃	C₂²	1	1	yes	characteristic
45	C₂×C₄×D₄×C₂₃	C₂²	1	1	yes	characteristic
46	C₂×C₂₃×#117	—	2	1	no	—
47	C₂×C₂₃×#117	C₂²	1	2	yes	—
48	C₂₃×#501	C₂²	1	2	yes	complemented
49	C₂₃×#498	C₂²	1	2	yes	complemented
50	C₂₃×#489	C₂²	1	2	yes	complemented
51	C₂₃×#487	C₂²	1	2	yes	complemented
52	C₂₃×#485	C₂²	1	4	yes	complemented
53	C₂₃×#485	C₂²	1	4	yes	complemented
54	C₂₃×#485	C₂²	1	4	yes	complemented
55	C₂₃×#484	C₂²	1	2	yes	—
56	C₂₃×#484	C₂²	1	1	yes	characteristic
57	C₂₃×#483	C₂²	1	2	yes	—
58	C₂₃×#483	C₂²	1	2	yes	—
59	C₂₃×#483	C₂²	1	2	yes	—
60	C₂₃×#482	C₂²	1	4	yes	complemented
61	C₂₃×#482	C₂²	1	4	yes	complemented
62	C₂₃×#481	C₂²	1	1	yes	characteristic
63	C₂₃×#481	C₂²	1	4	yes	complemented
64	C₂₃×#480	C₂²	1	2	yes	—
65	C₂₃×#478	C₂²	1	2	yes	complemented
66	C₂₃×#477	C₂²	1	2	yes	complemented
67	C₂₃×#476	C₂²	1	2	yes	complemented
68	C₂₃×#475	C₂²	1	4	yes	complemented
69	C₂₃×#474	C₂²	1	2	yes	complemented
70	C₂₃×#469	C₂²	1	4	yes	complemented
71	C₂₃×#468	C₂²	1	4	yes	complemented
72	C₂₃×#465	C₂²	1	4	yes	complemented
73	C₂₃×#465	C₂²	1	4	yes	complemented
74	C₂₃×#463	C₂²	1	2	yes	complemented
75	C₂₃×#461	C₂²	1	2	yes	complemented
76	C₂₃×#450	C₂²	1	1	yes	characteristic
77	C₂₃×#450	C₂²	1	2	yes	—
78	C₂₃×#449	C₂²	1	4	yes	complemented
79	C₂₃×#448	C₂²	1	4	yes	complemented
80	C₂₃×#447	C₂²	1	1	yes	characteristic
81	C₂₃×#440	C₂²	1	4	yes	complemented
82	C₄×SD₁₆×C₂₃	C₂²	1	2	yes	complemented
83	C₄×D₈×C₂₃	C₂²	1	2	yes	complemented
84	C₂₃×#436	C₂²	1	2	yes	complemented
85	C₂₃×#435	C₂²	1	4	yes	complemented
86	C₈×D₄×C₂₃	C₂²	1	2	yes	complemented
87	C₂₃×#432	C₂²	1	1	yes	characteristic
88	C₂₃×#431	C₂²	1	1	yes	characteristic
89	C₂₃×#428	C₂²	1	4	yes	complemented
90	C₂₃×#427	C₂²	1	4	yes	complemented
91	C₂₃×#419	C₂²	1	4	yes	complemented
92	C₂₃×#416	C₂²	1	4	yes	complemented
93	C₂₃×#407	C₂²	1	2	yes	—
94	C₂×C₂₃×C₂²⋊C₈	C₂²	1	2	yes	—
95	C₂×#41×C₂₃	—	2	1	no	—
96	C₂×#41×C₂₃	C₂³	1	2	yes	—
97	C₂²×Q₈×C₂₃	—	2	1	no	—
98	C₂²×Q₈×C₂₃	C₂³	1	2	yes	—
99	C₂²×D₄×C₂₃	—	2	2	no	—
100	C₂²×D₄×C₂₃	D₄	1	1	yes	characteristic
101	C₂²×D₄×C₂₃	C₂³	1	1	yes	characteristic
102	C₂³×C₄×C₂₃	—	2	1	no	—
103	C₂³×C₄×C₂₃	C₂³	1	2	yes	—
104	C₂×SD₁₆×C₂₃	C₂³	1	2	yes	—
105	C₂×SD₁₆×C₂₃	C₂³	1	4	yes	—
106	C₂×D₈×C₂₃	C₂³	1	2	yes	—
107	C₂×M₁₆×C₂₃	C₂³	1	4	yes	—
108	C₂²×C₈×C₂₃	C₂³	1	4	yes	—
109	C₂₃×C₄⋊Q₈	—	2	1	no	—
110	C₂₃×C₄⋊Q₈	—	2	1	no	—
111	C₂₃×C₄⋊Q₈	—	2	1	no	—
112	C₂₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
113	C₂₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
114	C₂₃×C₄⋊Q₈	C₂³	1	2	yes	—
115	C₂₃×C₄⋊Q₈	C₂³	1	2	yes	—
116	C₂₃×#126	—	2	2	no	—
117	C₂₃×#126	—	2	2	no	—
118	C₂₃×#126	—	2	1	no	—
119	C₂₃×#125	—	2	2	no	—
120	C₂₃×#125	—	2	1	no	—
121	C₂₃×#125	C₂³	1	1	yes	characteristic
122	C₂₃×#124	—	2	1	no	—
123	C₂₃×#124	—	2	2	no	—
124	C₂₃×#124	—	2	4	no	—
125	C₂₃×#124	—	2	4	no	—
126	C₂₃×#124	—	2	4	no	—
127	C₂₃×#124	—	2	4	no	—
128	C₂₃×#124	C₂³	1	1	yes	characteristic
129	C₂₃×#123	—	2	2	no	—
130	C₂₃×#123	—	2	1	no	—
131	C₂₃×#123	—	2	2	no	—
132	C₂₃×#123	—	2	2	no	—
133	C₂₃×#123	—	2	2	no	—
134	C₂₃×C₂²⋊Q₈	—	2	2	no	—
135	C₂₃×C₂²⋊Q₈	—	2	1	no	—
136	C₂₃×C₂²⋊Q₈	—	2	2	no	—
137	C₂₃×C₂²⋊Q₈	—	2	1	no	—
138	C₂₃×C₂²⋊Q₈	—	2	2	no	—
139	C₂₃×C₂²⋊Q₈	—	2	2	no	—
140	C₂₃×C₂²⋊Q₈	C₂³	1	2	yes	—
141	C₂₃×C₂²⋊Q₈	C₂³	1	2	yes	—
142	C₂₃×C₂²⋊Q₈	C₂³	1	2	yes	—
143	C₂₃×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
144	C₂₃×C₂²⋊Q₈	C₂³	1	2	yes	—
145	C₂₃×#121	—	2	1	no	—
146	C₂₃×#121	—	2	2	no	—
147	C₂₃×#121	—	2	2	no	—
148	C₂₃×#121	—	2	2	no	—
149	C₂₃×#121	—	2	4	no	—
150	C₂₃×#121	—	2	2	no	—
151	C₂₃×#121	—	2	2	no	—
152	C₂₃×#121	C₂³	1	2	yes	—
153	C₂₃×#121	C₂³	1	4	yes	—
154	C₂₃×#121	C₂³	1	4	yes	—
155	C₂₃×#121	C₂³	1	1	yes	characteristic
156	C₂₃×#120	—	2	2	no	—
157	C₄×Q₈×C₂₃	—	2	1	no	—
158	C₄×Q₈×C₂₃	—	2	1	no	—
159	C₄×Q₈×C₂₃	C₂³	1	2	yes	—
160	C₄×Q₈×C₂₃	C₂³	1	1	yes	characteristic
161	C₄×D₄×C₂₃	—	2	1	no	—
162	C₄×D₄×C₂₃	—	2	2	no	—
163	C₄×D₄×C₂₃	—	2	1	no	—
164	C₄×D₄×C₂₃	—	2	2	no	—
165	C₄×D₄×C₂₃	—	2	2	no	—
166	C₄×D₄×C₂₃	—	2	1	no	—
167	C₄×D₄×C₂₃	—	2	1	no	—
168	C₄×D₄×C₂₃	D₄	1	1	yes	characteristic
169	C₄×D₄×C₂₃	D₄	1	2	yes	—
170	C₄×D₄×C₂₃	D₄	1	1	yes	characteristic
171	C₄×D₄×C₂₃	C₂³	1	1	yes	characteristic
172	C₄×D₄×C₂₃	C₂³	1	2	yes	—
173	C₄×D₄×C₂₃	C₂³	1	2	yes	—
174	C₄×D₄×C₂₃	C₂³	1	1	yes	characteristic
175	C₄×D₄×C₂₃	C₂³	1	1	yes	characteristic
176	C₄×D₄×C₂₃	C₂³	1	2	yes	—
177	C₂₃×#117	—	2	1	no	—
178	C₂₃×#117	—	2	2	no	—
179	C₂₃×#117	—	2	2	no	—
180	C₂₃×#117	—	2	2	no	—
181	C₂₃×#117	—	2	4	no	—
182	C₂₃×#117	—	2	2	no	—
183	C₂₃×#117	—	2	2	no	—
184	C₂₃×#117	—	2	1	no	—
185	C₂₃×#117	C₂³	1	2	yes	—
186	C₂₃×#117	C₂³	1	4	yes	—
187	C₂₃×#117	C₂³	1	4	yes	—
188	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
189	C₂×C₄⋊C₄×C₂₃	—	2	2	no	—
190	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
191	C₂×C₄⋊C₄×C₂₃	D₄	1	1	yes	characteristic
192	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
193	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
194	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
195	C₂×C₂²⋊C₄×C₂₃	—	2	2	no	—
196	C₂×C₂²⋊C₄×C₂₃	—	2	2	no	—
197	C₂×C₂²⋊C₄×C₂₃	—	2	2	no	—
198	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
199	C₂×C₂²⋊C₄×C₂₃	D₄	1	2	yes	—
200	C₂×C₄²×C₂₃	—	2	2	no	—
201	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
202	C₂₃×#107	C₂³	1	4	yes	—
203	C₂₃×#107	C₂³	1	4	yes	—
204	C₂₃×#107	C₂³	1	2	yes	—
205	C₂₃×#106	C₂³	1	2	yes	—
206	C₂₃×#106	C₂³	1	4	yes	—
207	C₂₃×#106	C₂³	1	4	yes	—
208	C₂₃×#106	C₂³	1	4	yes	—
209	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
210	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
211	C₂₃×#103	C₂³	1	4	yes	—
212	C₂₃×#103	C₂³	1	4	yes	—
213	C₂₃×#103	C₂³	1	2	yes	—
214	C₂₃×#103	C₂³	1	4	yes	—
215	C₂₃×#103	C₂³	1	4	yes	—
216	C₂₃×#102	C₂³	1	2	yes	—
217	C₂₃×#102	C₂³	1	4	yes	—
218	C₂₃×#102	C₂³	1	2	yes	—
219	C₂₃×#102	C₂³	1	2	yes	—
220	C₂₃×#102	C₂³	1	4	yes	—
221	C₂₃×C₂²⋊C₈	C₂³	1	1	yes	characteristic
222	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
223	C₂₃×C₂²⋊C₈	C₂³	1	4	yes	—
224	C₂₃×C₂²⋊C₈	C₂³	1	1	yes	characteristic
225	C₂₃×C₂²⋊C₈	C₂³	1	4	yes	—
226	C₂₃×#97	C₂³	1	2	yes	—
227	C₄×C₈×C₂₃	C₂³	1	2	yes	—
228	C₂⁴×C₂₃	—	2	1	no	—
229	C₂⁴×C₂₃	C₂×D₄	1	2	yes	—
230	#41×C₂₃	—	4	4	no	—
231	#41×C₂₃	—	4	4	no	—
232	C₂×Q₈×C₂₃	—	2	1	no	—
233	C₂×Q₈×C₂₃	—	2	2	no	—
234	C₂×Q₈×C₂₃	—	2	2	no	—
235	C₂×Q₈×C₂₃	—	2	2	no	—
236	C₂×Q₈×C₂₃	—	4	4	no	—
237	C₂×Q₈×C₂₃	—	8	2	no	—
238	C₂×Q₈×C₂₃	C₂⁴	1	1	yes	characteristic
239	C₂×Q₈×C₂₃	C₂⁴	1	2	yes	—
240	C₂×D₄×C₂₃	—	2	1	no	—
241	C₂×D₄×C₂₃	—	2	2	no	—
242	C₂×D₄×C₂₃	—	2	2	no	—
243	C₂×D₄×C₂₃	—	2	4	no	—
244	C₂×D₄×C₂₃	—	2	4	no	—
245	C₂×D₄×C₂₃	—	2	1	no	—
246	C₂×D₄×C₂₃	—	4	2	no	—
247	C₂×D₄×C₂₃	—	4	2	no	—
248	C₂×D₄×C₂₃	—	8	4	no	—
249	C₂×D₄×C₂₃	C₂×D₄	1	1	yes	characteristic
250	C₂×D₄×C₂₃	C₂×D₄	1	1	yes	characteristic
251	C₂×D₄×C₂₃	C₂×D₄	1	2	yes	—
252	C₂×D₄×C₂₃	C₂⁴	1	1	yes	characteristic
253	C₂×D₄×C₂₃	C₂⁴	1	2	yes	—
254	C₂²×C₄×C₂₃	—	2	1	no	—
255	C₂²×C₄×C₂₃	—	2	2	no	—
256	C₂²×C₄×C₂₃	—	2	2	no	—
257	C₂²×C₄×C₂₃	—	2	2	no	—
258	C₂²×C₄×C₂₃	—	2	1	no	—
259	C₂²×C₄×C₂₃	—	2	2	no	—
260	C₂²×C₄×C₂₃	—	2	2	no	—
261	C₂²×C₄×C₂₃	—	2	2	no	—
262	C₂²×C₄×C₂₃	—	4	4	no	—
263	C₂²×C₄×C₂₃	—	4	4	no	—
264	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
265	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
266	C₂²×C₄×C₂₃	C₂×D₄	1	2	yes	—
267	C₂²×C₄×C₂₃	C₂×D₄	1	2	yes	—
268	C₂²×C₄×C₂₃	C₂×D₄	1	2	yes	—
269	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
270	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
271	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
272	SD₁₆×C₂₃	—	4	2	no	—
273	SD₁₆×C₂₃	—	4	4	no	—
274	D₈×C₂₃	—	4	2	no	—
275	M₁₆×C₂₃	—	4	4	no	—
276	C₂×C₈×C₂₃	—	4	4	no	—
277	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
278	C₂×C₈×C₂₃	C₂⁴	1	4	yes	—
279	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
280	C₄⋊C₄×C₂₃	—	2	1	no	—
281	C₄⋊C₄×C₂₃	—	2	2	no	—
282	C₄⋊C₄×C₂₃	—	2	2	no	—
283	C₄⋊C₄×C₂₃	—	2	2	no	—
284	C₄⋊C₄×C₂₃	—	2	1	no	—
285	C₄⋊C₄×C₂₃	—	2	2	no	—
286	C₄⋊C₄×C₂₃	—	2	2	no	—
287	C₄⋊C₄×C₂₃	—	2	1	no	—
288	C₄⋊C₄×C₂₃	—	2	2	no	—
289	C₄⋊C₄×C₂₃	—	2	2	no	—
290	C₄⋊C₄×C₂₃	—	2	1	no	—
291	C₄⋊C₄×C₂₃	—	2	1	no	—
292	C₄⋊C₄×C₂₃	—	2	1	no	—
293	C₄⋊C₄×C₂₃	—	2	2	no	—
294	C₄⋊C₄×C₂₃	—	2	1	no	—
295	C₄⋊C₄×C₂₃	—	2	2	no	—
296	C₄⋊C₄×C₂₃	—	2	1	no	—
297	C₄⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
298	C₄⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
299	C₄⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
300	C₄⋊C₄×C₂₃	C₂⁴	1	1	yes	characteristic
301	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
302	C₄⋊C₄×C₂₃	C₂⁴	1	1	yes	characteristic
303	C₄⋊C₄×C₂₃	C₂⁴	1	4	yes	—
304	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
305	C₂²⋊C₄×C₂₃	—	2	1	no	—
306	C₂²⋊C₄×C₂₃	—	2	4	no	—
307	C₂²⋊C₄×C₂₃	—	2	4	no	—
308	C₂²⋊C₄×C₂₃	—	2	2	no	—
309	C₂²⋊C₄×C₂₃	—	2	2	no	—
310	C₂²⋊C₄×C₂₃	—	2	2	no	—
311	C₂²⋊C₄×C₂₃	—	2	2	no	—
312	C₂²⋊C₄×C₂₃	—	2	2	no	—
313	C₂²⋊C₄×C₂₃	—	2	4	no	—
314	C₂²⋊C₄×C₂₃	—	2	4	no	—
315	C₂²⋊C₄×C₂₃	—	2	2	no	—
316	C₂²⋊C₄×C₂₃	—	2	2	no	—
317	C₂²⋊C₄×C₂₃	—	2	1	no	—
318	C₂²⋊C₄×C₂₃	—	2	1	no	—
319	C₂²⋊C₄×C₂₃	—	2	1	no	—
320	C₂²⋊C₄×C₂₃	—	2	2	no	—
321	C₂²⋊C₄×C₂₃	—	2	1	no	—
322	C₂²⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
323	C₂²⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
324	C₂²⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
325	C₂²⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
326	C₄²×C₂₃	—	2	4	no	—
327	C₄²×C₂₃	—	2	4	no	—
328	C₄²×C₂₃	—	2	2	no	—
329	C₄²×C₂₃	—	2	2	no	—
330	C₄²×C₂₃	—	2	1	no	—
331	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
332	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
333	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
334	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
335	#61731	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
336	C₂³×C₂₃	—	2	4	no	—
337	C₂³×C₂₃	—	2	1	no	—
338	C₂³×C₂₃	—	2	2	no	—
339	C₂³×C₂₃	—	4	2	no	—
340	C₂³×C₂₃	—	4	2	no	—
341	C₂³×C₂₃	—	4	2	no	—
342	C₂³×C₂₃	—	4	2	no	—
343	C₂³×C₂₃	—	4	2	no	—
344	C₂³×C₂₃	C₂²×D₄	1	2	yes	—
345	C₂³×C₂₃	C₂²×D₄	1	2	yes	—
346	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
347	Q₈×C₂₃	—	2	2	no	—
348	Q₈×C₂₃	—	2	4	no	—
349	Q₈×C₂₃	—	4	2	no	—
350	Q₈×C₂₃	—	8	2	no	—
351	Q₈×C₂₃	—	8	2	no	—
352	Q₈×C₂₃	—	8	2	no	—
353	D₄×C₂₃	—	2	2	no	—
354	D₄×C₂₃	—	2	2	no	—
355	D₄×C₂₃	—	2	2	no	—
356	D₄×C₂₃	—	2	2	no	—
357	D₄×C₂₃	—	2	2	no	—
358	D₄×C₂₃	—	4	2	no	—
359	D₄×C₂₃	—	4	2	no	—
360	D₄×C₂₃	—	4	4	no	—
361	D₄×C₂₃	—	4	2	no	—
362	D₄×C₂₃	—	8	4	no	—
363	D₄×C₂₃	—	8	4	no	—
364	D₄×C₂₃	—	8	2	no	—
365	C₂×C₄×C₂₃	—	2	2	no	—
366	C₂×C₄×C₂₃	—	2	2	no	—
367	C₂×C₄×C₂₃	—	2	4	no	—
368	C₂×C₄×C₂₃	—	2	4	no	—
369	C₂×C₄×C₂₃	—	2	2	no	—
370	C₂×C₄×C₂₃	—	2	2	no	—
371	C₂×C₄×C₂₃	—	2	1	no	—
372	C₂×C₄×C₂₃	—	2	2	no	—
373	C₂×C₄×C₂₃	—	2	4	no	—
374	C₂×C₄×C₂₃	—	2	1	no	—
375	C₂×C₄×C₂₃	—	2	2	no	—
376	C₂×C₄×C₂₃	—	2	1	no	—
377	C₂×C₄×C₂₃	—	4	2	no	—
378	C₂×C₄×C₂₃	—	4	2	no	—
379	C₂×C₄×C₂₃	—	4	2	no	—
380	C₂×C₄×C₂₃	—	4	4	no	—
381	C₂×C₄×C₂₃	—	4	2	no	—
382	C₂×C₄×C₂₃	—	4	4	no	—
383	C₂×C₄×C₂₃	—	4	4	no	—
384	C₂×C₄×C₂₃	—	4	4	no	—
385	C₂×C₄×C₂₃	—	4	2	no	—
386	C₂×C₄×C₂₃	—	8	2	no	—
387	C₂×C₄×C₂₃	—	8	2	no	—
388	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
389	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
390	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
391	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
392	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
393	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
394	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
395	C₂×C₄×C₂₃	C₂⁵	1	1	yes	characteristic
396	C₈×C₂₃	—	2	2	no	—
397	C₈×C₂₃	—	2	4	no	—
398	C₈×C₂₃	—	2	2	no	—
399	#3520	C₂×C₂₃	1	1	yes	characteristic, complemented
400	C₂×#555	C₂×C₂₃	1	1	yes	characteristic, complemented
401	#3354	C₂×C₂₃	1	2	yes	complemented
402	#3348	C₂×C₂₃	1	4	yes	complemented
403	#3340	C₂×C₂₃	1	2	yes	complemented
404	#3329	C₂×C₂₃	1	2	yes	complemented
405	#3321	C₂×C₂₃	1	4	yes	complemented
406	#3303	C₂×C₂₃	1	2	yes	complemented
407	#3238	C₂×C₂₃	1	1	yes	characteristic, complemented
408	#3229	C₂×C₂₃	1	1	yes	characteristic, complemented
409	#3194	C₂×C₂₃	1	2	yes	complemented
410	#3187	C₂×C₂₃	1	2	yes	complemented
411	#3110	C₂×C₂₃	1	1	yes	characteristic, complemented
412	#3105	C₂×C₂₃	1	1	yes	characteristic, complemented
413	#3095	C₂×C₂₃	1	2	yes	complemented
414	#3091	C₂×C₂₃	1	2	yes	complemented
415	#2974	C₂×C₂₃	1	1	yes	characteristic, complemented
416	C₂²×C₂₃	—	2	1	no	—
417	C₂²×C₂₃	—	2	1	no	—
418	C₂²×C₂₃	—	2	2	no	—
419	C₂²×C₂₃	—	2	2	no	—
420	C₂²×C₂₃	—	2	2	no	—
421	C₂²×C₂₃	—	2	2	no	—
422	C₂²×C₂₃	—	2	2	no	—
423	C₂²×C₂₃	—	2	2	no	—
424	C₂²×C₂₃	—	4	1	no	—
425	C₂²×C₂₃	—	4	2	no	—
426	C₂²×C₂₃	—	4	2	no	—
427	C₂²×C₂₃	—	4	1	no	—
428	C₂²×C₂₃	—	4	1	no	—
429	C₂²×C₂₃	—	4	2	no	—
430	C₂²×C₂₃	—	8	4	no	—
431	C₂²×C₂₃	—	8	4	no	—
432	C₂²×C₂₃	#577	1	2	yes	—
433	C₂²×C₂₃	C₂³×D₄	1	1	yes	characteristic
434	C₄×C₂₃	—	2	1	no	—
435	C₄×C₂₃	—	2	2	no	—
436	C₄×C₂₃	—	2	2	no	—
437	C₄×C₂₃	—	2	1	no	—
438	C₄×C₂₃	—	2	1	no	—
439	C₄×C₂₃	—	2	1	no	—
440	C₄×C₂₃	—	4	2	no	—
441	C₄×C₂₃	—	4	1	no	—
442	C₄×C₂₃	—	4	2	no	—
443	C₄×C₂₃	—	4	1	no	—
444	C₄×C₂₃	—	4	2	no	—
445	C₄×C₂₃	—	4	4	no	—
446	C₄×C₂₃	—	4	1	no	—
447	C₄×C₂₃	#575	1	2	yes	—
448	C₄×C₂₃	#585	1	2	yes	—
449	#556	C₂²×C₂₃	1	1	yes	characteristic, complemented
450	#555	—	2	1	no	—
451	#555	—	2	2	no	—
452	#555	—	2	1	no	—
453	#555	C₂²×C₂₃	1	2	yes	—
454	#555	C₂²×C₂₃	1	2	yes	—
455	#555	C₂²×C₂₃	1	4	yes	—
456	#554	—	2	1	no	—
457	#552	C₂²×C₂₃	1	2	yes	complemented
458	#551	—	2	2	no	—
459	D₄×Q₈	C₂²×C₂₃	1	1	yes	characteristic, complemented
460	#548	C₂²×C₂₃	1	2	yes	complemented
461	#547	C₂²×C₂₃	1	1	yes	characteristic, complemented
462	#547	C₂²×C₂₃	1	1	yes	characteristic, complemented
463	#546	—	2	1	no	—
464	#542	—	2	1	no	—
465	#539	—	2	2	no	—
466	#533	C₂²×C₂₃	1	1	yes	characteristic
467	C₂×C₄⋊Q₈	C₂²×C₂₃	1	1	yes	characteristic
468	#529	C₂²×C₂₃	1	1	yes	characteristic
469	C₂×#124	—	2	2	no	—
470	#525	C₂²×C₂₃	1	2	yes	—
471	C₂×C₂²⋊Q₈	C₂²×C₂₃	1	2	yes	—
472	C₂×#121	—	2	1	no	—
473	C₂×#121	C₂²×C₂₃	1	2	yes	—
474	#520	—	2	1	no	—
475	C₂×C₄×D₄	C₂²×C₂₃	1	1	yes	characteristic
476	C₂×C₄×D₄	C₂²×C₂₃	1	1	yes	characteristic
477	C₂×#117	—	2	1	no	—
478	C₂×#117	C₂²×C₂₃	1	2	yes	—
479	#501	C₂²×C₂₃	1	2	yes	complemented
480	#498	C₂²×C₂₃	1	2	yes	complemented
481	#489	C₂²×C₂₃	1	2	yes	complemented
482	#487	C₂²×C₂₃	1	2	yes	complemented
483	#485	C₂²×C₂₃	1	4	yes	complemented
484	#485	C₂²×C₂₃	1	4	yes	complemented
485	#485	C₂²×C₂₃	1	4	yes	complemented
486	#484	C₂²×C₂₃	1	2	yes	—
487	#484	C₂²×C₂₃	1	1	yes	characteristic
488	#483	C₂²×C₂₃	1	2	yes	—
489	#483	C₂²×C₂₃	1	2	yes	—
490	#483	C₂²×C₂₃	1	2	yes	—
491	#482	C₂²×C₂₃	1	4	yes	complemented
492	#482	C₂²×C₂₃	1	4	yes	complemented
493	#481	C₂²×C₂₃	1	1	yes	characteristic
494	#481	C₂²×C₂₃	1	4	yes	complemented
495	#480	C₂²×C₂₃	1	2	yes	—
496	#478	C₂²×C₂₃	1	2	yes	complemented
497	#477	C₂²×C₂₃	1	2	yes	complemented
498	#476	C₂²×C₂₃	1	2	yes	complemented
499	#475	C₂²×C₂₃	1	4	yes	complemented
500	#474	C₂²×C₂₃	1	2	yes	complemented
501	#469	C₂²×C₂₃	1	4	yes	complemented
502	#468	C₂²×C₂₃	1	4	yes	complemented
503	#465	C₂²×C₂₃	1	4	yes	complemented
504	#465	C₂²×C₂₃	1	4	yes	complemented
505	#463	C₂²×C₂₃	1	2	yes	complemented
506	#461	C₂²×C₂₃	1	2	yes	complemented
507	#450	C₂²×C₂₃	1	1	yes	characteristic
508	#450	C₂²×C₂₃	1	2	yes	—
509	#449	C₂²×C₂₃	1	4	yes	complemented
510	#448	C₂²×C₂₃	1	4	yes	complemented
511	#447	C₂²×C₂₃	1	1	yes	characteristic
512	#440	C₂²×C₂₃	1	4	yes	complemented
513	C₄×SD₁₆	C₂²×C₂₃	1	2	yes	complemented
514	C₄×D₈	C₂²×C₂₃	1	2	yes	complemented
515	#436	C₂²×C₂₃	1	2	yes	complemented
516	#435	C₂²×C₂₃	1	4	yes	complemented
517	C₈×D₄	C₂²×C₂₃	1	2	yes	complemented
518	#432	C₂²×C₂₃	1	1	yes	characteristic
519	#431	C₂²×C₂₃	1	1	yes	characteristic
520	#428	C₂²×C₂₃	1	4	yes	complemented
521	#427	C₂²×C₂₃	1	4	yes	complemented
522	#419	C₂²×C₂₃	1	4	yes	complemented
523	#416	C₂²×C₂₃	1	4	yes	complemented
524	#407	C₂²×C₂₃	1	2	yes	—
525	C₂×C₂²⋊C₈	C₂²×C₂₃	1	2	yes	—
526	C₂×C₂₃	—	2	2	no	—
527	C₂×C₂₃	—	4	2	no	—
528	C₂×C₂₃	—	4	2	no	—
529	C₂×C₂₃	—	8	1	no	—
530	C₂×C₂₃	—	8	2	no	—
531	C₂×C₂₃	#3485	1	1	yes	characteristic
532	C₂×C₂₃	C₂×#575	1	1	yes	characteristic
533	C₂×C₂₃	C₂×#577	1	1	yes	characteristic
534	C₂×#41	—	2	1	no	—
535	C₂×#41	C₂³×C₂₃	1	2	yes	—
536	C₂²×Q₈	—	2	1	no	—
537	C₂²×Q₈	C₂³×C₂₃	1	2	yes	—
538	C₂²×D₄	—	2	2	no	—
539	C₂²×D₄	D₄×C₂₃	1	1	yes	characteristic
540	C₂²×D₄	C₂³×C₂₃	1	1	yes	characteristic
541	C₂³×C₄	—	2	1	no	—
542	C₂³×C₄	C₂³×C₂₃	1	2	yes	—
543	C₂×SD₁₆	C₂³×C₂₃	1	2	yes	—
544	C₂×SD₁₆	C₂³×C₂₃	1	4	yes	—
545	C₂×D₈	C₂³×C₂₃	1	2	yes	—
546	C₂×M₁₆	C₂³×C₂₃	1	4	yes	—
547	C₂²×C₈	C₂³×C₂₃	1	4	yes	—
548	C₄⋊Q₈	—	2	1	no	—
549	C₄⋊Q₈	—	2	1	no	—
550	C₄⋊Q₈	—	2	1	no	—
551	C₄⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
552	C₄⋊Q₈	C₂³×C₂₃	1	2	yes	—
553	C₄⋊Q₈	C₂³×C₂₃	1	2	yes	—
554	C₄⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
555	#126	—	2	2	no	—
556	#126	—	2	2	no	—
557	#126	—	2	1	no	—
558	#125	—	2	2	no	—
559	#125	—	2	1	no	—
560	#125	C₂³×C₂₃	1	1	yes	characteristic
561	#124	—	2	1	no	—
562	#124	—	2	4	no	—
563	#124	—	2	4	no	—
564	#124	—	2	4	no	—
565	#124	—	2	4	no	—
566	#124	—	2	2	no	—
567	#124	C₂³×C₂₃	1	1	yes	characteristic
568	#123	—	2	2	no	—
569	#123	—	2	2	no	—
570	#123	—	2	1	no	—
571	#123	—	2	2	no	—
572	#123	—	2	2	no	—
573	C₂²⋊Q₈	—	2	2	no	—
574	C₂²⋊Q₈	—	2	2	no	—
575	C₂²⋊Q₈	—	2	1	no	—
576	C₂²⋊Q₈	—	2	2	no	—
577	C₂²⋊Q₈	—	2	1	no	—
578	C₂²⋊Q₈	—	2	2	no	—
579	C₂²⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
580	C₂²⋊Q₈	C₂³×C₂₃	1	2	yes	—
581	C₂²⋊Q₈	C₂³×C₂₃	1	2	yes	—
582	C₂²⋊Q₈	C₂³×C₂₃	1	2	yes	—
583	C₂²⋊Q₈	C₂³×C₂₃	1	2	yes	—
584	#121	—	2	2	no	—
585	#121	—	2	2	no	—
586	#121	—	2	4	no	—
587	#121	—	2	2	no	—
588	#121	—	2	1	no	—
589	#121	—	2	2	no	—
590	#121	—	2	2	no	—
591	#121	C₂³×C₂₃	1	4	yes	—
592	#121	C₂³×C₂₃	1	4	yes	—
593	#121	C₂³×C₂₃	1	1	yes	characteristic
594	#121	C₂³×C₂₃	1	2	yes	—
595	#120	—	2	2	no	—
596	C₄×Q₈	—	2	1	no	—
597	C₄×Q₈	—	2	1	no	—
598	C₄×Q₈	C₂³×C₂₃	1	1	yes	characteristic
599	C₄×Q₈	C₂³×C₂₃	1	2	yes	—
600	C₄×D₄	—	2	1	no	—
601	C₄×D₄	—	2	2	no	—
602	C₄×D₄	—	2	2	no	—
603	C₄×D₄	—	2	1	no	—
604	C₄×D₄	—	2	2	no	—
605	C₄×D₄	—	2	1	no	—
606	C₄×D₄	—	2	1	no	—
607	C₄×D₄	D₄×C₂₃	1	1	yes	characteristic
608	C₄×D₄	D₄×C₂₃	1	2	yes	—
609	C₄×D₄	D₄×C₂₃	1	1	yes	characteristic
610	C₄×D₄	C₂³×C₂₃	1	2	yes	—
611	C₄×D₄	C₂³×C₂₃	1	2	yes	—
612	C₄×D₄	C₂³×C₂₃	1	1	yes	characteristic
613	C₄×D₄	C₂³×C₂₃	1	1	yes	characteristic
614	C₄×D₄	C₂³×C₂₃	1	1	yes	characteristic
615	C₄×D₄	C₂³×C₂₃	1	2	yes	—
616	#117	—	2	2	no	—
617	#117	—	2	2	no	—
618	#117	—	2	1	no	—
619	#117	—	2	2	no	—
620	#117	—	2	4	no	—
621	#117	—	2	2	no	—
622	#117	—	2	2	no	—
623	#117	—	2	1	no	—
624	#117	C₂³×C₂₃	1	4	yes	—
625	#117	C₂³×C₂₃	1	4	yes	—
626	#117	C₂³×C₂₃	1	2	yes	—
627	C₂×C₄⋊C₄	—	2	1	no	—
628	C₂×C₄⋊C₄	—	2	2	no	—
629	C₂×C₄⋊C₄	—	2	1	no	—
630	C₂×C₄⋊C₄	D₄×C₂₃	1	1	yes	characteristic
631	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
632	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
633	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
634	C₂×C₂²⋊C₄	—	2	2	no	—
635	C₂×C₂²⋊C₄	—	2	2	no	—
636	C₂×C₂²⋊C₄	—	2	2	no	—
637	C₂×C₂²⋊C₄	—	2	1	no	—
638	C₂×C₂²⋊C₄	D₄×C₂₃	1	2	yes	—
639	C₂×C₄²	—	2	2	no	—
640	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
641	#107	C₂³×C₂₃	1	4	yes	—
642	#107	C₂³×C₂₃	1	4	yes	—
643	#107	C₂³×C₂₃	1	2	yes	—
644	#106	C₂³×C₂₃	1	2	yes	—
645	#106	C₂³×C₂₃	1	4	yes	—
646	#106	C₂³×C₂₃	1	4	yes	—
647	#106	C₂³×C₂₃	1	4	yes	—
648	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
649	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
650	#103	C₂³×C₂₃	1	4	yes	—
651	#103	C₂³×C₂₃	1	4	yes	—
652	#103	C₂³×C₂₃	1	2	yes	—
653	#103	C₂³×C₂₃	1	4	yes	—
654	#103	C₂³×C₂₃	1	4	yes	—
655	#102	C₂³×C₂₃	1	2	yes	—
656	#102	C₂³×C₂₃	1	4	yes	—
657	#102	C₂³×C₂₃	1	2	yes	—
658	#102	C₂³×C₂₃	1	2	yes	—
659	#102	C₂³×C₂₃	1	4	yes	—
660	C₂²⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
661	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
662	C₂²⋊C₈	C₂³×C₂₃	1	4	yes	—
663	C₂²⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
664	C₂²⋊C₈	C₂³×C₂₃	1	4	yes	—
665	#97	C₂³×C₂₃	1	2	yes	—
666	C₄×C₈	C₂³×C₂₃	1	2	yes	—
667	C₂₃	#61731	1	1	yes	characteristic, direct product factor, Sylow
668	C₂⁴	—	2	1	no	—
669	C₂⁴	C₂×D₄×C₂₃	1	2	yes	—
670	#41	—	4	4	no	—
671	#41	—	4	4	no	—
672	C₂×Q₈	—	2	1	no	—
673	C₂×Q₈	—	2	2	no	—
674	C₂×Q₈	—	2	2	no	—
675	C₂×Q₈	—	2	2	no	—
676	C₂×Q₈	—	4	4	no	—
677	C₂×Q₈	—	8	2	no	—
678	C₂×Q₈	C₂⁴×C₂₃	1	1	yes	characteristic
679	C₂×Q₈	C₂⁴×C₂₃	1	2	yes	—
680	C₂×D₄	—	2	1	no	—
681	C₂×D₄	—	2	2	no	—
682	C₂×D₄	—	2	2	no	—
683	C₂×D₄	—	2	4	no	—
684	C₂×D₄	—	2	4	no	—
685	C₂×D₄	—	2	1	no	—
686	C₂×D₄	—	4	2	no	—
687	C₂×D₄	—	4	2	no	—
688	C₂×D₄	—	8	4	no	—
689	C₂×D₄	C₂×D₄×C₂₃	1	1	yes	characteristic
690	C₂×D₄	C₂×D₄×C₂₃	1	1	yes	characteristic
691	C₂×D₄	C₂×D₄×C₂₃	1	2	yes	—
692	C₂×D₄	C₂⁴×C₂₃	1	1	yes	characteristic
693	C₂×D₄	C₂⁴×C₂₃	1	2	yes	—
694	C₂²×C₄	—	2	1	no	—
695	C₂²×C₄	—	2	2	no	—
696	C₂²×C₄	—	2	2	no	—
697	C₂²×C₄	—	2	2	no	—
698	C₂²×C₄	—	2	1	no	—
699	C₂²×C₄	—	2	2	no	—
700	C₂²×C₄	—	2	2	no	—
701	C₂²×C₄	—	2	2	no	—
702	C₂²×C₄	—	4	4	no	—
703	C₂²×C₄	—	4	4	no	—
704	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
705	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
706	C₂²×C₄	C₂×D₄×C₂₃	1	2	yes	—
707	C₂²×C₄	C₂×D₄×C₂₃	1	2	yes	—
708	C₂²×C₄	C₂×D₄×C₂₃	1	2	yes	—
709	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
710	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
711	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
712	SD₁₆	—	4	2	no	—
713	SD₁₆	—	4	4	no	—
714	D₈	—	4	2	no	—
715	M₁₆	—	4	4	no	—
716	C₂×C₈	—	4	4	no	—
717	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
718	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
719	C₂×C₈	C₂⁴×C₂₃	1	4	yes	—
720	C₄⋊C₄	—	2	1	no	—
721	C₄⋊C₄	—	2	2	no	—
722	C₄⋊C₄	—	2	2	no	—
723	C₄⋊C₄	—	2	2	no	—
724	C₄⋊C₄	—	2	1	no	—
725	C₄⋊C₄	—	2	2	no	—
726	C₄⋊C₄	—	2	2	no	—
727	C₄⋊C₄	—	2	1	no	—
728	C₄⋊C₄	—	2	2	no	—
729	C₄⋊C₄	—	2	2	no	—
730	C₄⋊C₄	—	2	1	no	—
731	C₄⋊C₄	—	2	1	no	—
732	C₄⋊C₄	—	2	1	no	—
733	C₄⋊C₄	—	2	2	no	—
734	C₄⋊C₄	—	2	1	no	—
735	C₄⋊C₄	—	2	2	no	—
736	C₄⋊C₄	—	2	1	no	—
737	C₄⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
738	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
739	C₄⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
740	C₄⋊C₄	C₂⁴×C₂₃	1	1	yes	characteristic
741	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
742	C₄⋊C₄	C₂⁴×C₂₃	1	1	yes	characteristic
743	C₄⋊C₄	C₂⁴×C₂₃	1	4	yes	—
744	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
745	C₂²⋊C₄	—	2	1	no	—
746	C₂²⋊C₄	—	2	4	no	—
747	C₂²⋊C₄	—	2	4	no	—
748	C₂²⋊C₄	—	2	2	no	—
749	C₂²⋊C₄	—	2	2	no	—
750	C₂²⋊C₄	—	2	2	no	—
751	C₂²⋊C₄	—	2	2	no	—
752	C₂²⋊C₄	—	2	2	no	—
753	C₂²⋊C₄	—	2	4	no	—
754	C₂²⋊C₄	—	2	4	no	—
755	C₂²⋊C₄	—	2	2	no	—
756	C₂²⋊C₄	—	2	2	no	—
757	C₂²⋊C₄	—	2	1	no	—
758	C₂²⋊C₄	—	2	1	no	—
759	C₂²⋊C₄	—	2	1	no	—
760	C₂²⋊C₄	—	2	2	no	—
761	C₂²⋊C₄	—	2	1	no	—
762	C₂²⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
763	C₂²⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
764	C₂²⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
765	C₂²⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
766	C₄²	—	2	4	no	—
767	C₄²	—	2	4	no	—
768	C₄²	—	2	2	no	—
769	C₄²	—	2	2	no	—
770	C₄²	—	2	1	no	—
771	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
772	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
773	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
774	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
775	C₂³	—	2	4	no	—
776	C₂³	—	2	1	no	—
777	C₂³	—	2	2	no	—
778	C₂³	—	4	2	no	—
779	C₂³	—	4	2	no	—
780	C₂³	—	4	2	no	—
781	C₂³	—	4	2	no	—
782	C₂³	—	4	2	no	—
783	C₂³	C₂²×D₄×C₂₃	1	2	yes	—
784	C₂³	C₂²×D₄×C₂₃	1	2	yes	—
785	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
786	Q₈	—	2	2	no	—
787	Q₈	—	2	4	no	—
788	Q₈	—	4	2	no	—
789	Q₈	—	8	2	no	—
790	Q₈	—	8	2	no	—
791	Q₈	—	8	2	no	—
792	D₄	—	2	2	no	—
793	D₄	—	2	2	no	—
794	D₄	—	2	2	no	—
795	D₄	—	2	2	no	—
796	D₄	—	2	2	no	—
797	D₄	—	4	2	no	—
798	D₄	—	4	2	no	—
799	D₄	—	4	4	no	—
800	D₄	—	4	2	no	—
801	D₄	—	8	4	no	—
802	D₄	—	8	4	no	—
803	D₄	—	8	2	no	—
804	C₂×C₄	—	2	2	no	—
805	C₂×C₄	—	2	2	no	—
806	C₂×C₄	—	2	4	no	—
807	C₂×C₄	—	2	4	no	—
808	C₂×C₄	—	2	2	no	—
809	C₂×C₄	—	2	2	no	—
810	C₂×C₄	—	2	1	no	—
811	C₂×C₄	—	2	2	no	—
812	C₂×C₄	—	2	4	no	—
813	C₂×C₄	—	2	1	no	—
814	C₂×C₄	—	2	2	no	—
815	C₂×C₄	—	2	1	no	—
816	C₂×C₄	—	4	2	no	—
817	C₂×C₄	—	4	2	no	—
818	C₂×C₄	—	4	2	no	—
819	C₂×C₄	—	4	4	no	—
820	C₂×C₄	—	4	2	no	—
821	C₂×C₄	—	4	4	no	—
822	C₂×C₄	—	4	4	no	—
823	C₂×C₄	—	4	4	no	—
824	C₂×C₄	—	4	2	no	—
825	C₂×C₄	—	8	2	no	—
826	C₂×C₄	—	8	2	no	—
827	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
828	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
829	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
830	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
831	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
832	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
833	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
834	C₂×C₄	C₂⁵×C₂₃	1	1	yes	characteristic
835	C₈	—	2	2	no	—
836	C₈	—	2	4	no	—
837	C₈	—	2	2	no	—
838	C₂²	—	2	1	no	—
839	C₂²	—	2	1	no	—
840	C₂²	—	2	2	no	—
841	C₂²	—	2	2	no	—
842	C₂²	—	2	2	no	—
843	C₂²	—	2	2	no	—
844	C₂²	—	2	2	no	—
845	C₂²	—	2	2	no	—
846	C₂²	—	4	1	no	—
847	C₂²	—	4	2	no	—
848	C₂²	—	4	2	no	—
849	C₂²	—	4	1	no	—
850	C₂²	—	4	1	no	—
851	C₂²	—	4	2	no	—
852	C₂²	—	8	4	no	—
853	C₂²	—	8	4	no	—
854	C₂²	C₂₃×#577	1	2	yes	—
855	C₂²	C₂³×D₄×C₂₃	1	1	yes	characteristic
856	C₄	—	2	1	no	—
857	C₄	—	2	2	no	—
858	C₄	—	2	2	no	—
859	C₄	—	2	1	no	—
860	C₄	—	2	1	no	—
861	C₄	—	2	1	no	—
862	C₄	—	4	2	no	—
863	C₄	—	4	1	no	—
864	C₄	—	4	2	no	—
865	C₄	—	4	1	no	—
866	C₄	—	4	2	no	—
867	C₄	—	4	4	no	—
868	C₄	—	4	1	no	—
869	C₄	C₂₃×#575	1	2	yes	—
870	C₄	C₂₃×#585	1	2	yes	—
871	C₂	—	2	2	no	—
872	C₂	—	4	2	no	—
873	C₂	—	4	2	no	—
874	C₂	—	8	2	no	—
875	C₂	—	8	1	no	—
876	C₂	C₂₃×#3485	1	1	yes	characteristic
877	C₂	C₂×C₂₃×#575	1	1	yes	characteristic
878	C₂	C₂×C₂₃×#577	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₂₃	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₂₃
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₂₃ ◁ C₂×C₄×D₄×C₂₃ ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
1. C₂₃×#3520	C₂	semidirect
2. C₂×C₂₃×#555	C₂	semidirect
3. C₂₃×#3354	C₂	semidirect
4. C₂₃×#3348	C₂	semidirect
5. C₂₃×#3340	C₂	semidirect
6. C₂₃×#3329	C₂	semidirect
7. C₂₃×#3321	C₂	semidirect
8. C₂₃×#3303	C₂	semidirect
9. C₂₃×#3238	C₂	semidirect
10. C₂₃×#3229	C₂	semidirect
11. C₂₃×#3194	C₂	semidirect
12. C₂₃×#3187	C₂	semidirect
13. C₂₃×#3110	C₂	semidirect
14. C₂₃×#3105	C₂	semidirect
15. C₂₃×#3095	C₂	semidirect
16. C₂₃×#3091	C₂	semidirect
17. C₂₃×#2974	C₂	semidirect
18. C₂₃×#556	C₂²	semidirect
26. C₂₃×#552	C₂²	semidirect
28. D₄×Q₈×C₂₃	C₂²	semidirect
29. C₂₃×#548	C₂²	semidirect
30. C₂₃×#547	C₂²	semidirect
31. C₂₃×#547	C₂²	semidirect
48. C₂₃×#501	C₂²	semidirect
49. C₂₃×#498	C₂²	semidirect
50. C₂₃×#489	C₂²	semidirect
51. C₂₃×#487	C₂²	semidirect
52. C₂₃×#485	C₂²	semidirect
53. C₂₃×#485	C₂²	semidirect
54. C₂₃×#485	C₂²	semidirect
60. C₂₃×#482	C₂²	semidirect
61. C₂₃×#482	C₂²	semidirect
63. C₂₃×#481	C₂²	semidirect
65. C₂₃×#478	C₂²	semidirect
66. C₂₃×#477	C₂²	semidirect
67. C₂₃×#476	C₂²	semidirect
68. C₂₃×#475	C₂²	semidirect
69. C₂₃×#474	C₂²	semidirect
70. C₂₃×#469	C₂²	semidirect
71. C₂₃×#468	C₂²	semidirect
72. C₂₃×#465	C₂²	semidirect
73. C₂₃×#465	C₂²	semidirect
74. C₂₃×#463	C₂²	semidirect
75. C₂₃×#461	C₂²	semidirect
78. C₂₃×#449	C₂²	semidirect
79. C₂₃×#448	C₂²	semidirect
81. C₂₃×#440	C₂²	semidirect
82. C₄×SD₁₆×C₂₃	C₂²	semidirect
83. C₄×D₈×C₂₃	C₂²	semidirect
84. C₂₃×#436	C₂²	semidirect
85. C₂₃×#435	C₂²	semidirect
86. C₈×D₄×C₂₃	C₂²	semidirect
89. C₂₃×#428	C₂²	semidirect
90. C₂₃×#427	C₂²	semidirect
91. C₂₃×#419	C₂²	semidirect
92. C₂₃×#416	C₂²	semidirect
335. #61731	C₂₃	direct (N × H)
399. #3520	C₂×C₂₃	semidirect
400. C₂×#555	C₂×C₂₃	semidirect
401. #3354	C₂×C₂₃	semidirect
402. #3348	C₂×C₂₃	semidirect
403. #3340	C₂×C₂₃	semidirect
404. #3329	C₂×C₂₃	semidirect
405. #3321	C₂×C₂₃	semidirect
406. #3303	C₂×C₂₃	semidirect
407. #3238	C₂×C₂₃	semidirect
408. #3229	C₂×C₂₃	semidirect
409. #3194	C₂×C₂₃	semidirect
410. #3187	C₂×C₂₃	semidirect
411. #3110	C₂×C₂₃	semidirect
412. #3105	C₂×C₂₃	semidirect
413. #3095	C₂×C₂₃	semidirect
414. #3091	C₂×C₂₃	semidirect
415. #2974	C₂×C₂₃	semidirect
449. #556	C₂²×C₂₃	semidirect
457. #552	C₂²×C₂₃	semidirect
459. D₄×Q₈	C₂²×C₂₃	semidirect
460. #548	C₂²×C₂₃	semidirect
461. #547	C₂²×C₂₃	semidirect
462. #547	C₂²×C₂₃	semidirect
479. #501	C₂²×C₂₃	semidirect
480. #498	C₂²×C₂₃	semidirect
481. #489	C₂²×C₂₃	semidirect
482. #487	C₂²×C₂₃	semidirect
483. #485	C₂²×C₂₃	semidirect
484. #485	C₂²×C₂₃	semidirect
485. #485	C₂²×C₂₃	semidirect
491. #482	C₂²×C₂₃	semidirect
492. #482	C₂²×C₂₃	semidirect
494. #481	C₂²×C₂₃	semidirect
496. #478	C₂²×C₂₃	semidirect
497. #477	C₂²×C₂₃	semidirect
498. #476	C₂²×C₂₃	semidirect
499. #475	C₂²×C₂₃	semidirect
500. #474	C₂²×C₂₃	semidirect
501. #469	C₂²×C₂₃	semidirect
502. #468	C₂²×C₂₃	semidirect
503. #465	C₂²×C₂₃	semidirect
504. #465	C₂²×C₂₃	semidirect
505. #463	C₂²×C₂₃	semidirect
506. #461	C₂²×C₂₃	semidirect
509. #449	C₂²×C₂₃	semidirect
510. #448	C₂²×C₂₃	semidirect
512. #440	C₂²×C₂₃	semidirect
513. C₄×SD₁₆	C₂²×C₂₃	semidirect
514. C₄×D₈	C₂²×C₂₃	semidirect
515. #436	C₂²×C₂₃	semidirect
516. #435	C₂²×C₂₃	semidirect
517. C₈×D₄	C₂²×C₂₃	semidirect
520. #428	C₂²×C₂₃	semidirect
521. #427	C₂²×C₂₃	semidirect
522. #419	C₂²×C₂₃	semidirect
523. #416	C₂²×C₂₃	semidirect
667. C₂₃	#61731	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂₃×#3520	2
C₂×C₂₃×#555	2
C₂₃×#3354	2
C₂₃×#3348	2
C₂₃×#3340	2
C₂₃×#3329	2
C₂₃×#3321	2
C₂₃×#3303	2
C₂₃×#3238	2
C₂₃×#3229	2
C₂₃×#3194	2
C₂₃×#3187	2
C₂₃×#3110	2
C₂₃×#3105	2
C₂₃×#3095	2
C₂₃×#3091	2
C₂₃×#2974	2
#61731	23

Subgroups — C23×#61731 #19209357

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#61731 #19209357